A new look at survey propagation and its generalizations

13 years 4 months ago

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This article provides a new conceptual perspective on survey propagation, which is an iterative algorithm recently introduced by the statistical physics community that is very effective in solving random k-SAT problems even with densities close to the satisﬁability threshold. We ﬁrst describe how any SAT formula can be associated with a novel family of Markov random ﬁelds (MRFs), parameterized by a real number ρ ∈ [0, 1]. We then show that applying belief propagation—a wellknown “message-passing” technique for estimating marginal probabilities—to this family of MRFs recovers a known family of algorithms, ranging from pure survey propagation at one extreme (ρ = 1) to standard belief propagation on the uniform distribution over SAT assignments at the other extreme (ρ = 0). Conﬁgurations in these MRFs have a natural interpretation as partial satisﬁability assignments, on which a partial order can be deﬁned. We isolate cores as minimal elements in this partial orde...

Elitza N. Maneva, Elchanan Mossel, Martin J. Wainw

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